It’s a brand new year. Congratulations, you’ve made it this far. Good for you. I hope you enjoyed the holiday season and I wish you an extraordinary new year. I can’t… well… think if any other way to spark this, so let’s just get on with it.
God is a mathematician. Ignore for one moment the theosophical implications of a statement like that. I am personally not a believer, but that’s not the point. My point is that Mathematics is the language of the universe. When all physical knowledge is whittled down to its simplest form, it is understood mathematically. Maths allows us to expand beyond our senses and perceive the universe in ways that may be considered non-intuitive.
Mathematics, while considered a science, predates science and is the basic language that all the physical sciences either speak, or can learn from. There are those, me included, who think mathematics should be taught as a liberal art. Math is more than a science, more than a process; it’s a way of thinking. Whether she knows it or not, the mathematician is a philosopher. The Pythagoreans from whom we get the Pythagorean Theorem were more a philosophical cult than a technical movement.
Math is a subject that while drilled into us through rote memorization of formulas, is actually an artifact of our ability to think outside the box. Math has always been the result of thought processes. It seems obvious when you think about it. Math is the process by which we found meaningful answers to practical problems. How do we equally divide land that has an odd shape, for example? People are left with the pressure of solving basic daily problems related to trade and commerce and even law. And with most of the math being incidental or accidental, such as the inadvertent math used in constructing your family hut or distributing adequate portions of food to each family member.
[pullquote_left]We have found the perfect education system to instill arithmophobia in children and we carry it into adulthood.[/pullquote_left]Today you count on your fingers or in your head and teach children how to count without a second thought to the extraordinary breakthrough that is Combinatorics (essentially, this is counting, and its problems tend to arise in “pure” mathematics like algebra, geometry, topology, etc.). Counting, and a number system, any number system, represent one of the earliest “killer apps” of the human brain (some might argue that language was the first. I would consider tool making as an advanced app but not a killer app that separates us from most other creatures). Math is non-intuitive and requires a logical leap for even its most basic parts.
Look at a clock and while you might grasp how it works mechanically (maybe you don’t), your mind fails to grasp the pure and elegant math that its machinations communicate. You understand the passage of time through your experiences, but you can’t intuitively understand time the way math can. Have you ever looked at the number zero? Have you ever thought about the staggering amount of creativity required to make that logical leap; the idea that, in counting, there can be a “nothing”. In the history of math, the invention of zero is not as old as geometry and perhaps only slightly older than pure algebra. It’s basically a young discovery compared to many human discoveries.
I imagine the epiphany that invented zero going something like this:
Person A: “wait, so if I have five bushels, and you take away all of them, I have no bushels.”
Person B: “Yes. And?”
Person A: “Well… how do I… umm… indicate that? I mean, what do I take back?”
Person B: “You take back nothing.”
Person A: “Yes but… I mean… but… I know I go with nothing, but…”
Round and round they go until a realization is made. Incidentally, the concept of zero first emerged among the people of the Indus valley, also responsible for Algebra. Nothing is something. It is something with no value. However, imagine the greater leap required to invent negative numbers. Once the mind is wrapped around the idea of the void, imagine the brute force creativity required to imagine that one can have less than nothing. Taking the example above, person B cannot take away more than 5 bushels from Person A since he doesn’t have more than 5 bushels. He can owe extra bushels on a later date, but he cannot give them now. On a practical level, negatives would have made no sense. But then math would have suffered under a time constraint.
That is, until someone made a logical leap and said, “what if I imagine next month was this month? I could balance accounts in real time.” Person A may realistically have 0 bushels right now but on “paper” he can be shown to have a deficit. It’s hard to convey how groundbreaking this idea is, since we use it without a second thought, but I assure you, the invention of zero and negative numbers represent massive philosophical leaps; leaps that seem obvious in hindsight. Not all logical leaps seem obvious and we still have a hard time wrapping our minds around many things long after we’ve proven them correct.
It bothers me that Math isn’t given both a liberal art and a science path the way business degrees can often come as a bachelor of arts or a bachelor of science. Math changes the way you think, it makes you comfortable with the non-intuitive, and it allows your tiny brain to comprehend the vastness of the universe. Whether it’s plotting your course on that road trip, or poker night with the fellas; you’re doing math or thinking in math without realizing it.
Why do people fear Math so much? School has made it boring, repetitive, and needlessly hard. A common question is “what will I use this for?” This question shows the first thing that’s wrong with the way math is taught. You shouldn’t have to ask. Math shouldn’t be about memorizing formulas, it should be about practical problem solving and logical thinking. Right now Physics has become math having fun, as has chemistry and all these other subjects (these other subjects aren’t entirely fun either, but you get my point). We have made math, beyond general counting, impractical.
We have found the perfect education system to instill arithmophobia in children and we carry it into adulthood. Everyone believes math is hard. Math is many things but not hard. It’s something we do without thinking. It’s our most primal language, beautified with symbols. At the same time, math IS hard. It requires a logical leap that I promise you, will become easier and more natural. To see the world through a mathematician’s eye is to see with more than 5 senses. The world becomes so much bigger and so much more wondrous. From the early days when you were taught to do basic math, you were made to feel that your understanding of it was inadequate, so the first step to overcome your irrational fear (pardon the pun) of math, is to master the basics. Learn to do math rapidly in your head. It won’t take you more than a few hours total, spread over days or weeks.
This may be enough for most people, but I hope it’s just be the beginning. It does offend me a little when I hear from education reformists that Math isn’t that important and that we should focus more on the arts. I don’t disagree with the need to focus more on these other things, but the argument that math is unimportant is silly. What needs to be changed is HOW we teach maths and sciences. We need a return of the philosophies and liberal arts aspects of math. We need a way to inject the joy of it. Imagine an artist, already imbued with extraordinary vision, able to comprehend the awesomeness of the world around her. Imagine the ballerina in a more perfect mental sync with her pirouetting body, making play things out of gravity. Imagine a more logical populace, in-tune with the calculus that animates its life (and the wonders it will do for navigating traffic).
I’m not talking about a society of Mentats, nor am I looking for everyone to get a math degree. We would get so much further if people just stopped fearing math and learned the myriad ways it could improve their current lives. The ability to think, even on a basic level, mathematically, would change the way we view our world, our place in the world, economics, even health. Math has been busy building and running the universe. It has been busy doing what it does, arguably indifferent to the greater good, but still benefiting the greater good. Perhaps it’s time to stop telling people what math does for the world and start telling them what math can do for them. Perhaps it’s time for a selfish mathematics.